Morphologies of Division and Union: A Field-Theoretic Unification of Nuclear Fission, Mitotic Dynamics, and Chromosomal Fusion

The physical universe exhibits a striking topological self-similarity across vast scales of magnitude. Whether observing the splitting of a heavy atomic nucleus or the division of a eukaryotic cell, one witnesses the fundamental drama of a coherent whole losing stability, deforming, and rupturing into daughter entities. Conversely, the forging of heavier elements in the heart of a star and the rearrangement of genetic architecture in Robertsonian translocations represent the inverse topology: the overcoming of a repulsive barrier to achieve a unified, albeit sometimes unstable, new state. This report responds to a unique theoretical challenge: to construct a rigorous mathematical isomorphism between the mitosis of a biological cell and the nuclear fission of a particle; to formalize this analogy into a "biological Quantum Field Theory" (bQFT) using the tools of second quantization; and finally, to derive a comparative mathematical description of fusion, contrasting the high-energy nucleosynthesis of hydrogen with the enzymatic recombination of chromosomes. The analysis proceeds in four distinct phases. First, we establish the macroscopic correspondence between the Nuclear Liquid Drop Model (LDM) and the biophysics of the cell, mapping the phenomenological parameters of the Bethe-Weizsäcker mass formula to the viscoelastic properties of the cytoplasm and cortex. Second, we transcend this mean-field description to derive a microscopic field theory. By applying the Doi-Peliti formalism to the stochastic master equations of cell division, we demonstrate how the creation and annihilation operators of quantum mechanics naturally describe the birth and death of biological lineages. Third, we investigate the kinetics of fusion, contrasting the quantum tunneling of protons through the Coulomb barrier (governed by the Gamow window) with the "enzymatic tunneling" of chromosomes through the telomeric barrier (governed by the kinetics of Non-Homologous End Joining). Finally, we synthesize these insights into a unified comparative formula that quantifies the probability amplitudes of these disparate fusion events. This work draws upon a diverse array of disciplines, including high-energy particle physics, non-equilibrium statistical mechanics, active matter hydrodynamics, and molecular cytogenetics, to provide an exhaustive theoretical treatment of biological division and reunion.